A078951 Primes p such that the differences between the 5 consecutive primes starting with p are (2,6,6,6).

3299, 5099, 6359, 19469, 30089, 53609, 63689, 71339, 77549, 80909, 105359, 119549, 152939, 186869, 292469, 302969, 344249, 348239, 408209, 415949, 652739, 707669, 737039, 792689, 818339, 831539, 852749, 886979, 910199, 974969, 1072829, 1152629, 1290629, 1368329

Offset

1,1

Comments

Equivalently, primes p such that p, p+2, p+8, p+14 and p+20 are consecutive primes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) == 29 (mod 30). - Amiram Eldar, Feb 21 2025

Example

5099 is in the sequence since 5099, 5101 = 5099 + 2, 5107 = 5099 + 8, 5113 = 5099 + 14 and 5119 = 5099 + 20 are consecutive primes.

Mathematica

Select[Partition[Prime[Range[50000]], 5, 1], Differences[#] == {2, 6, 6, 6} &][[;; , 1]] (* Amiram Eldar, Feb 21 2025 *)

Prog

(PARI) list(lim) = {my(p1 = 2, p2 = 3, p3 = 5, p4 = 7); forprime(p5 = 11, lim, if(p2 - p1 == 2 && p3 - p2 == 6 && p4 - p3 == 6 && p5 - p4 == 6, print1(p1, ", ")); p1 = p2; p2 = p3; p3 = p4; p4 = p5); } \\ Amiram Eldar, Feb 21 2025

Crossrefs

Subsequence of A078849. - R. J. Mathar, May 06 2017

Cf. A001223, A078866, A078867, A078946-A078971, A022006, A022007.

Sequence in context: A068755 A330253 A242862 * A236660 A106721 A078969

Adjacent sequences: A078948 A078949 A078950 * A078952 A078953 A078954

Keyword

nonn

Author

Labos Elemer, Dec 19 2002

Extensions

Edited by Dean Hickerson, Dec 20 2002

Status

approved